BHF Integrated Mathematical Modeling and Imaging Project

Project Aims

It is well known that the passive and active behavior of cardiac muscle changes with disease. This change can occur at multiple scales — from the level of the cell, level of tissue, up to the whole organ. The passive behavior of the heart is known to change due to fibrosis and other extracellular matrix changes which can also yield large-scale anatomical change. The active behavior of the heart can also change, with changes in cross-bridge proteins, alterations in calcium re-absorption in the SR, tissue-level conduction alterations, etc. The net effect of these is a fundamental shift in the passive and active properties of the heart at the organ-scale which yield a change in the ability of our bodies most valuable muscle to do its job — effectively deliver blood to the body.

The aim of this study is to use Integrated Mathematical modeling and Medical Imaging (IMMI) together to better understand the effect of pathology on the mechanics — passive and active — of the heart. From imaging we can observe the kinematic motion of the heart, however the cost of this motion in terms of force, work and energy requires knowledge of the hearts underlying biomechanics. This knowledge can be obtained through integration between model and data.

Study Design

In the IMMI study, we are recruiting 40 participants: 20 normal volunteers and 20 patients diagnosed with dilated cardiomyopathy. Data about the heart of each participant is collected under rest conditions. Following this acquisition, participants are given a fast acting beta-blocker, allowing data to be collected under controlled conditions causing reduced heart rate and reduced contractility. Comprehensive mathematical models are then constructed for each participant in both states, and the mechanics of their hearts analyzed.

Medical Imaging

For this study, a comprehensive dataset is gathered for each participant. Here we acquire comprehensive 4D Phase contrast MRI, 3D Tagged MRI, 3D SSFP, CINE Stacks, Aortic Outflow, IVC / SVC Inflow as well as pressure measurements from a radial cuff. This wealth of data provides a comprehensive overview of each participant’s heart which we must integrate into our modeling framework.

Data Assimilation

A core aspect of this project is the assimilation of this comprehensive data into the model. This requires image / data registration, anatomical model fabrication from images, extraction of kinematic data from images, and model parameterization. For this workflow we rely on a series of tools:

IRTK Toolkit – Developed at Imperial College

CardioViz – Developed at iNRIA

Model parameterization is then achieved in CHeart using implemented Kalman filters (mainly the Reduced Order Unscented Kalman Filter developed by Dominique Chapelle at iNRIA), enabling us to construct models that integrate all sources of patient data. Multiple models – LV and biventricular – are constructed to maximize usage of the available data.

Core to this project is the fidelity of the model produced. Here we have constructed models which aim to balance practical identifiability (e.g. uniqueness of parameters) with model fidelity in order to identify key parameters which govern the passive and active behavior of the cardiac muscle.

Modeling

Final parameterized mathematical models may then be simulated in CHeart. Here we use a number of unique elements in the code to successfully model cardiac behavior in vivo — including specialized boundary conditions, material laws, etc. The output of these models then allow us to compare metrics of stress, work, and function between normal individuals and patients as well as study the adaptability of both groups (under beta-blockade).